Predefined-Time Frequency Estimation of Biased Sinusoidal Signals

This brief proposes an observer-based adaptive approach for predefined-time parameter estimation of biased sinusoidal signals. By employing this observer-based adaptive strategy, the parameter estimation is successfully achieved within the predefined-time. Notably, the convergence time remains unchanged regardless of variations in the system's parameters, where the convergence time is dependent on the system's parameters. In addition, the proposed scheme considers the presence of measurement noise in the output signal, while ensuring that the frequency estimator maintains input-to-state stability (ISS). By leveraging the Lyapunov theorem, the stability of the proposed approach is assured. Furthermore, the effectiveness of the proposed method is demonstrated through a numerical example that successfully achieves the desired level of performance in frequency estimation.